Bandwidth excitation

HSQC rather than HMQC-based transfer schemes have recently in particular been employed in various indirectly detected two- and three-dimensional 111/X/Y correlation experiments involving multi-step coherence-transfer in either direction.38 40 43 44 The application of PFG s appears to be essential to obtain a sufficiently clean spectrum that is free of artefacts, and in many cases the pulse sequence shows only a satisfactory performance if composite pulses, with a larger excitation bandwidth than normal ones, are employed.21,38,39,43 The pulse schemes yield generally phase-sensitive spectra with pure absorptive lines and do not suffer from splitting or broadening of the cross peaks as a consequence of the undesired evolution... 

The amplitude modulated pulses may require special equipment such as a waveform generator which, however, has become a standard constituent of the modem commercial spectrometers. The amplitude modulated pulses are usually windowless and the sidebands produced by these pulses, in most cases, are very weak and can be neglected. The simplest amplitude modulated pulses are Gaussian pulse, sine pulse or sine-square pulse [1]. The main drawback of these simple shapes is that they produce a phase gradient over the excitation bandwidth and their excitation profiles are non-uniform over the bandwidth of interest. The amplitude modulated pulses can easily be shifted off-resonance by applying a phase ramp over the pulse according to equation (4). 

Figure 3.4. A single monochromatic radiofrequency pulse has an effective excitation bandwidth that depends inversely on the duration of the pulse. A short intense pulse is therefore able to excite over a wide frequency window (a), whereas a longer weaker pulse provides a more selective excitation profile (b).

For those spins further from resonance, the angle 0 becomes greater and the net rotation toward the x-y plane diminishes until, in the limit, 0 becomes 90 . In this case the bulk magnetisation vector simply remains along the -f-z-axis and thus experiences no excitation at all. In other words, the nuclei resonate outside the excitation bandwidth of the pulse. Since an off-resonance vector is driven away from the y-axis during the pulse it also acquires a (frequency dependent) phase difference relative to the on-resonance vector (Fig. 3.6). This is usually small and an approximately linear function of frequency so can be corrected by phase adjustment of the final spectrum (Section 3.2.8). 

Universal pulses act equally on any initial magnetisation state whereas excitation and inversion pulses are designed to act on longitudinal magnetisation only. The bandwidth factor is the product of the pulse duration. At, and the excitation bandwidth, Af, which is here defined as the excitation window over which the pulse is at least 70% effective (net pulse amplitude within 3 dB of the maximum other publications may define this value for higher levels and so quote smaller bandwidth factors). Use this factor to estimate the appropriate pulse duration for the desired bandwidth. The attenuation factor is used for approximate power calibration and represents the amount by which the transmitter output should be increased over that of a soft rectangular pulse of equal duration. The Gaussian based profiles are truncated at the 1% level. 

The excitation profile of soft pulses is defined by the duration of the pulse, these two factors sharing an inverse proportionality. More precisely, pulse shapes have associated with them a dimensionless bandwidth factor which is the product of the pulse duration. At, and its effective excitation bandwidth, Af, for a correctly calibrated pulse. This is fixed for any given pulse envelope, and... 

In the literature hard pulses and shaped pulses are usually treated as different entities such that any phase or amplitude modulation of hard pulses is neglected or assumed to be negligible whereas the phase and amplitude variation of a shaped pulse is always emphasized. The truth is that even hard pulses can have a significant phase and amplitude variation particularly at the extremes of their excitation bandwidth. For a comprehensive discussion the reader is referred to section 5.3.1. 

Mwtp)/( MWtp excitation bandwidth of a specific pulse depends only on... 

In complete analogy to NMR, FT EPR has been extended into two dimensions. Two-dimensional correlation spectroscopy (COSY) is essentially subject to the same restrictions regarding excitation bandwidth and detection deadtime as was described for one-dimensional FT EPR. In 2D-COSY EPR a second time dimension is added to the FID collection time by a preparatory pulse in front of the FID detection pulse and by variation of the evolution time between them (see figure B1.15.10(B)). The FID is recorded during the detection period of duration t, which begins with the second 7r/2-pulse. For each the FID is collected, then the phase of the first pulse is advanced by 90°, and a second set of FIDs is collected. The two sets of FIDs, whose amplitudes oscillate as functions of t, then undergo a two-dimensional complex Fourier transformation, generating a spectrum over the two frequency variables co and co,. 

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